Critical Path Method (CPM)

The critical path is the longest sequence of dependent activities from the start to the end of a project. Its length is the shortest possible project duration. Any delay to an activity on the critical path delays the whole project by the same amount; activities off the critical path have float (also called slack) — time they can slip without moving the end date.

What you need

• A list of activities (from your WBS).
• A duration estimate for each.
• The dependencies between them (most often finish-to-start).

Step 1: Draw the network

Use the activity-on-node method: each activity is a box, arrows show dependencies. Our example:

Step 2: Forward pass (earliest dates)

For each activity, Early Start (ES) = the largest Early Finish of its predecessors (0 for the first), and Early Finish (EF) = ES + duration.

• A: ES 0, EF 5 · B: 5–9 · C: 5–11 · D: 9–19 · E: 11–19 · H: 11–15
• F: ES = max(19, 19) = 19, EF 22 · G: 22–27 · I: ES = max(27, 15) = 27, EF 28

Project duration = 28 days.

Step 3: Backward pass (latest dates)

Starting from the end, Late Finish (LF) = the smallest Late Start of successors (project end for the last), and Late Start (LS) = LF − duration.

• I: 27–28 · G: 22–27 · F: 19–22 · D: 9–19 · E: 11–19 · B: 5–9
• H: LF = 27, LS = 23 · C: LF = min(LS of E = 11, LS of H = 23) = 11, LS 5 · A: 0–5

Step 4: Calculate float

Total float = LS − ES. Here every activity has zero float except H (23 − 11 = 12 days). That means there are two critical paths of 28 days: A→B→D→F→G→I and A→C→E→F→G→I. Two parallel critical paths are a warning sign — the project has no schedule buffer on either branch.

Check this example yourself in the critical path calculator (it loads as the default example).

Compressing the schedule

• Crashing: add resources to critical activities. Compare cost per day saved and crash the cheapest first.
• Fast-tracking: overlap activities that were sequential, e.g. start frontend build before UI design is fully signed off. Increases risk of rework.
• Reduce scope on the critical path, or move work off it.

After every change, recalculate: shortening one path often makes another one critical.

CPM vs PERT vs critical chain

CPM uses single-point duration estimates. PERT uses three-point estimates to model uncertainty. Critical chain project management adds resource constraints and pools contingency into shared buffers at the end of the chain rather than padding each task.